What is the relationship between corresponding sides, altitudes, and medians in similar triangles?
The ratio of their lengths is the same.
Similarity can be defined through a concept of scaling (see Unizor  "Geometry  Similarity").
Accordingly, all linear elements (sides, altitudes, medians, radiuses of inscribed and circumscribed circles etc.) of one triangle are scaled by the same scaling factor to be congruent to corresponding elements of another triangle. This scaling factor is the ratio between the lengths of all corresponding elements and is the same for all elements.
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In similar triangles:

Corresponding sides are proportional. This means that the ratio of corresponding sides in similar triangles is constant.

Altitudes are also proportional. The ratio of the lengths of corresponding altitudes in similar triangles is the same as the ratio of the lengths of corresponding sides.

Medians are also proportional. The ratio of the lengths of corresponding medians in similar triangles is the same as the ratio of the lengths of corresponding sides.
In summary, corresponding sides, altitudes, and medians of similar triangles are all proportional to each other.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 Triangle A has sides of lengths #36 ,24 #, and #16 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?
 A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #27 #, what is the length of side BC?
 A triangle has corners points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #10 #, what is the length of side BC?
 A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #45 #, what is the length of side BC?
 A triangle has corners at points A, B, and C. Side AB has a length of #27 #. The distance between the intersection of point A's angle bisector with side BC and point B is #15 #. If side AC has a length of #36 #, what is the length of side BC?
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